As the field of social robotics is growing, a consensus has been made on the design and implementation of robotic systems that are capable of adapting based on the user actions. These actions may be based on their emotions, personality or memory of past interactions. Therefore, we believe it is significant to report a review of the past research on the use of adaptive robots that have been utilised in various social environments. In this paper, we present a systematic review on the reported adaptive interactions across a number of domain areas during Human-Robot Interaction and also give future directions that can guide the design of future adaptive social robots. We conjecture that this will help towards achieving long-term applicability of robots in various social domains.